User blog:HowStrongIs/How Fast is Sonic in 1, 2, and 3? (Sonic the Hedgehog)
Since this is Classic Sonic, we'll have to use Classic Sonic's height, 0.818 m. In addition, despite what the title says I'm going to go ahead and put Sonic CD in here too. Also keep in mind that I will not be calculating Sonic's speed with any power ups or boosts from the environment. Just pure, base Sonic's speed on a flat terrain. ---- Sonic the Hedgehog Sonic 1 speed.gif The first game has few mechanics, so it's fairly easy to calculate. Just distance over time, really. Or we can calculate his speed from how fast he'd need to be going to loop like that. Using the first method, we can see that Sonic is 104 px tall. In the video we're using it takes him 0.4 s to cross this 344 px, or 2.71 m, gap. That gives us all the variables we need. With our other method, we can calculate how fast he'd need to be going by measuring the radius of the loop he goes through and assuming gravity is the same as our own. In here you can see the loop has a diameter of 370 px, or a radius of 185 px. This correlates to an actual distance of 1.46 m. Since we're assuming gravity is the same as our own, 9.81 m/s2, this gives us all the numbers we need. ---- v = d/t *d = 2.71 m *t = 0.4 s 2.71/0.4 = 6.78 m/s v = √5*g*r *g = 9.81 m/s2 *r = 1.46 m √5*9.81*1.46 = 8.46 m/s ---- So yeah, going by his observed speed he's just 6.78 m/s, but going by the speed needed to get through that loop under Earth's gravity he'd need to be moving at 8.46 m/s. This last bit isn't needed for the above calculation, but I will need it later and I'll be doing this calculation for all the other games as well. Sonic, while curled up into a ball, is 79 px in diameter. Since his height is 104 px/'0.818 m', this means his ball form is 0.621 m wide. ---- Sonic the Hedgehog 2 Sonic 2 spin dash.gif Sonic 2 loop.gif Sonic 2 speed.gif This is going to be about the same as the above, except now Sonic has a Spin Dash to take into account. Sonic, in this video, is 103 px tall. We can see that it takes Sonic 0.2 s to cross this 190 px, or 1.51 m, distance. This covers that area of discussion. We can also see that it takes Sonic 0.1 s to cross this 200 px, or 1.59 m, distance with his Spin Dash. From the same frame we can also determine that Sonic is 79 px/'0.627 m' wide when in his ball form, almost the exact same as he was before. Lastly, we can see that the loops in this game are 500 px in diameter, correlating to a radius of 250 px, or 1.99 m. ---- v = d/t *d = 1.51 m *t = 0.2 s 1.51/0.2 = 7.55 m/s for his running v = d/t *d = 1.59 m *t = 0.1 s 1.59/0.1 = 15.9 m/s for his Spin Dash v = √5*g*r *g = 9.81 m/s2 *r = 1.99 m √5*9.81*1.99 = 9.88 m/s to get through the loops ---- Sonic the Hedgehog 3 Sonic 3 speed.gif Sonic 3 tree run.gif Sonic 3 spin dash.gif So for this part of the blog we're mainly going to be using this video, with some guest appearances by this one. This section of the blog is also going to have the most math in it, because now we have four things to account for. Sonic's foot speed, Sonic's Spin Dash speed, Sonic's footspeed in set animations, and Sonic's speed to go through the loops. Starting with his foot speed, let's go ahead and establish that Sonic is 109 px tall in this game. We can see from the second video that it takes Sonic 0.4 s to cross this 380 px, or 2.85 m, distance. Moving on to his Spin Dash, it takes Sonic 0.13 s in the first video to cross this 226 px/'2.07 m' long distance. Now moving on to his speed in animations, we see Sonic run through a circular tree at high speeds early in the game. It takes him 0.48 s to run across the tree's full circumference, and we can see that the tree is, at most, 672 px in diameter. A little less due to the tree's thickness, but regardless, this gives us a radius of 2.52 m. Lastly, we have the loops. In this game, the loops are [https://howstrongis.wikia.com/wiki/File:Sonic_3_loop_distance.png 503 px] in diameter, or 1.89 m in radius. We can also see from the same picture that Sonic, in his ball form, is 79 px in diameter once more, meaning that the ball form in this game is 0.593 m across. With all this in mind, we can finally get our figures. ---- v = d/t *d = 2.85 m *t = 0.4 s 2.85/0.4 = 7.13 m/s for his foot speed v = d/t *d = 2.07 m *t = 0.13 s 2.07/0.13 = 15.9 m/s for his Spin Dash speed C = 2*pi*r *pi = 3.14 *r = 2.52 m 2*3.14*2.52 = 15.83 m v = d/t *d = 15.83 m *t = 0.48 s 15.83/0.48 = 33 m/s for his run through the tree (This should be a bit higher, but not much higher) v = √5*g*r *g = 9.81 m/s2 *r = 1.89 m √5*9.81*1.89 = 9.63 m/s to get through the loops ---- Sonic CD Sonic cd super peelout speed.gif Sonic cd loop.gif Sonic cd speed.gif This is our last game for this blog. All we need here is his foot speed, his Spin Dash speed, the speed of a new technique called the Super Peel-Out, and his speed when going through a loop. This game does have cutscenes we can calculate from, but we already did that in our last Sonic blog. In this video, we can see that Sonic is 102 px tall. It takes him 0.27 s to cross this 207 px/'1.66 m' long gap to the rock. So that gives us his normal foot speed. For his Spin Dash, it takes Sonic 0.24 s to cross this 410 px, or 3.29 m, long distance. As a side-note, his ball form is also, once again, 79 px tall, making it 0.634 m wide in actuality. In this video, we can see that Sonic is 110 px tall. When using Super Peel-Out, it takes Sonic 0.13 s to cross this 255 px, or 1.9 m, distance. Lastly, we need the size of the loops in this game. Going back to the first video, they're shown to be 500 px across, for a radius of 250 px, or 2 m. With all this out of the way we can finally end this blog. ---- v = d/t *d = 1.66 m *t = 0.27 s 1.66/0.27 = 6.15 m/s for his foot speed v = d/t *d = 3.29 m *t = 0.24 s 3.29/0.24 = 13.7 m/s for his Spin Dash speed v = d/t *d = 1.9 m *t = 0.13 s 1.9/0.13 = 14.6 m/s for his Super Peel-Out speed v = √5*g*r *g = 9.81 m/s2 *r = 2 m √5*9.81*2 = 9.91 m/s to get through the loops ---- Results Sonic the Hedgehog *Run Speed - 6.78 m/s *Loop Speed - 8.46 m/s *Ball Height - 0.621 m Sonic the Hedgehog 2 *Run Speed - 7.55 m/s *Spin Dash Speed - 15.9 m/s *Loop Speed - 9.88 m/s *Ball Height - 0.627 m Sonic the Hedgehog 3 *Run Speed - 7.13 m/s *Spin Dash Speed - 15.9 m/s *Tree Run Speed - 33 m/s< *Loop Speed - 9.63 m/s *Ball Height - 0.593 m Sonic CD *Run Speed - 6.15 m/s *Spin Dash Speed - 13.7 m/s *Super Peel-Out Speed - 14.6 m/s *Loop Speed - 9.91 m/s *Ball Height - 0.634 m Category:Blog posts Category:Calculation Category:How Fast is Sonic?